Regional income differences in the United States are starting to disappear, and the South, where incomes were only half the national average in 1929, stood at more than four-fifths in 1981, the Commerce Department reported yesterday.

The department's Bureau of Economic Analysis, in a study of per capita personal income over the last half-century, spelled out a trend that has been increasingly evident in recent years: the South, Rocky Mountain states, Plains and Southwest are still the poorest sections of the country, but they are much closer to the richer North than they were five decades ago.

Industry is growing faster in these previously lagging regions, and that tends to smooth out the differences.

The bureau found that the national average annual per capita personal income in 1929 was $697, with the northern sections as a group far above it (averaging 127 percent) and the South and other poor sections far below, at 64 percent of the national average.

By 1981, however, the northern sections averaged 106 percent of the $10,491 national average and the poorer regions had jumped to 92 percent.

The narrowing of the margin was most marked in the 12 southeastern states. In 1929 this section was the nation's poorest, with per capita personal income of only $366, far behind the Middle Atlantic region, which topped the nation at $963 per person.

By 1981, however, the Southeast, at $9,014 per person, was much closer to the $11,669 per capita income enjoyed by the Far West, now the national leader.

In 1981, the regions ranked as follows:

* Far West, $11,669 per person, 111 percent of the national average.

* Middle Atlantic, $11,301 per person, 108 percent.

* New England, $11,058, 105 percent.

* Great Lakes, $10,656, 102 percent.

* Southwest, $10,405, 99 percent.

* Plains, $10,270, 98 percent.

* Rocky Mountains, $10,056, 96 percent.

* Southeast, $9,014, 86 percent.

The bureau said that, in addition to a more favorable distribution of industry, the poorer regions were being helped by more uniform rates of income from dividends, interest, rents, welfare, Social Security and other transfer payments.

In 1929 New York was the state with the highest per capita personal income, but by 1981 it had dropped to eighth.

Excluding the District of Columbia, which is totally urban and has no rural region to pull down its numbers, and Alaska, which has a unique high-price, high-wage structure, Connecticut is now the highest state, at $12,816.

It is followed by New Jersey ($12,127) and California ($11,923).

Mississippi is poorest at $7,408, with South Carolina next poorest ($8,039) and Arkansas next ($8,044).

For the District of Columbia the per capita personal income in 1981 was $13,539. For Maryland, it was $11,477, ranking it seventh among the states, and for Virginia, $10,349, putting it 20th.